Slower rotation curves at centre

On galaxy rotation curves, the velocities of stars (or gas) rotating about their galactic centre remain fairly constant as the distance from the galactic centre increases.

But these rotation curves show a drop in rotation velocity towards the centre of the galaxy.

http://astro.berkeley.edu/~mwhite/darkmatter/rotcurve.html" [Broken]

I accept that at the centre the rotation velocity must be zero but just out from the centre, Kepler’s third law predicts that the velocities should be greatest and then fall off with increasing distance.

Does this velocity profile exist because the centre of galaxies up to about 6kpc (in the hyperlinked curve) are a bit like a solid mass?

Galactic rotation curves are determined by the distribution of mass throughout the galaxy.

Kepler's laws were derived empirically for the solar system where nearly all the mass is in the centre, in the Sun.

To obtain the typical galactic rotation curve, where for a large proportion of the radial distance the rotation velocity remains fairly constant, you need a lot of mass outside the visible galactic disk. This is one of the reasons it is believed galactic haloes contain a lot of Dark Matter.

As the radius approaches the centre you are leaving more and more mass outside that radius and the rotational velocity drops off, however often very near the centre it often starts to increase again indicating that there is often a large mass at the centre itself, most probably a massive Black Hole.

When the mass of a galaxy is worked out from the centre to a given radius r, the velocity of rotation is determined at that radius. Then using Kepler’s 3rd law, the inner mass can be determined. The outer mass (beyond the radius r) seems to be ignored.

Are you saying that near the centre of a galaxy where there is a higher density of mass that the above method is not valid?

Well, first it is the rotation velocity that is measured, using the slope of the red shift across the galactic disc as presented (projected) onto our celestial sphere.

Then the mass within that orbit can be calculated. If the outer mass is spherically distributed, symmetrically about the galactic centre the contributions from opposite sectors cancel themselves out and they can be ignored.

However, if they are not spherically distributed then they have to be taken into account, this is the case with real galaxies.

The actual Galaxy rotation curve is the data on which a model of the mass distribution has to be constructed.